Does anyone know whether law schools expect students to take money out of their IRAs (specifically, in my case, a Roth IRA) to put toward tuition? Do you think this would be an appropriate question to direct to specific institutions' financial aid offices?

The FAFSA does not include IRAs when calculating a student's EFC, but it looks like the Need Access form does ask for the balance of IRAs.

I have some cash in savings which I am considering attempting to "shelter" in my Roth IRA (a good idea even if I wasn't planning to go to law schools). But before I move it, I'm curious as to whether I'll be expected to use it anyway.

I think your best bet is to call your school's financial aid office and ask. Each school may consider it differently. I've put money in my Roth because, as you said, it's a good idea regardless and I know I can access my initial contributions without penalty if I need the money.